162. For the reaction A + B → 2C at a given temperature, the rate of disappearance of A is found to be 10^-2 moles L^–1 sec^–1. Calculate (i) rate of disappearance of B and (ii) rate of formation of C.

For  a given reaction 
A + B → 2C
we have given 
 the rate of disappearance of A is  10^-2 moles L^–1 sec^–1

(ii)
 rate of expression can be written as 

$\frac{-\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}=\frac{-d\left[B\right]}{dt}$

since rate of  disappearance of A is given to be 10^-2 moles L^–1 sec^–1
thus 
rate of  disappearance B 10^-2 moles L^–1 sec^–1


(iii)
$$\begin{gathered} \frac{\mathrm{d}\left[\mathrm{A}\right]}{\mathrm{dt}}= \frac{1}{2}\frac{d\left[C\right]}{dt} \\ as given \frac{\mathrm{d}\left[\mathrm{A}\right]}{dt}= {10}^{-2}moles L^{-1} se{c}^{-1} \\ thus \\ {10}^{-2}moles L^{-1} se{c}^{-1} = \frac{1}{2}\frac{d\left[C\right]}{dt} \\ \frac{d\left[C\right]}{dt}=2x{10}^{-2}moles L^{-1} se{c}^{-1} \end{gathered}$$
for Ans. (i) 10^–2 mol L^–1 sec^–1   (ii) 2 x 10^–2mole L^–1 sec^–1